The application of Boolean methods to the school time-tabling problem

Abstract

This study concerns itself with the application of Boolean techniques to the solution of the School Time-Tabling Problem. In particular, it involves a discussion of the manner in which all teaching conditions and restrictions within a school may be expressed in the form of Pseudo-Boolean Equations. Moreover, it seeks to outline how these Pseudo-Boolean Equations may be used to conduct a form-by-form tree-search of feasible and/or optimal timetables. This inevitably embraces a discussion of Boolean Algebra in its own right. A dual purpose is thus served. One obviously is academic ; the other is to dispel the apprehensions of the uninitiated to Boolean methods. Indeed, worked out examples will accompany all crucial steps in the argument. Furthermore, a complete glossary of symbols is provided. The primary function of Chapter I is the development of an accounting system which is then used to detect errors in the various data banks. A number of subsidiary functions are also served. Firstly, an introduction to Pseudo-Boolean Equations. Secondaly, the development of a consistent and workable nomenclature describing school activity. Finally, an introduction to the Time-Tabling Problem. The central theme of Chapter II is the concept of Data-Consistent-Infeasibilities. This concept, together with the nomenclature developed in the previous chapter, is used to generate Psudo-Boolean Conditions, every one of which must be satisfied by the feasible timetable. Chapter III illustrates the results of the previous two chapters. Finally, Chapter IV discusses the relative merits and short-comings associated with the alternative routes by which feasible timetables are generated.